Search Results (44)

We derive a Nambu–Jona-Lasinio (NJL) model from a non-local gauge theory and show that it has confining properties at low energies. In particular, we present an extended approach to non-local QCD and a complete revision of the technique of Bender, Milton and Savage applied to non-local theories, providing a set of Dyson–Schwinger equations in differential form. In the local case, we obtain closed-form solutions in the simplest case of the scalar field and extend it to the Yang–Mills field. In general, for non-local theories, we use a perturbative technique and a Fourier series and show how higher-order harmonics are heavily damped due to the presence of the non-local factor. The spectrum of the theory is analysed for the non-local Yang–Mills sector and found to be in agreement with the local results on the lattice in the limit of the non-locality mass parameter running to infinity. In the non-local case, we confine ourselves to a non-locality mass that is sufficiently large compared to the mass scale arising from the integration of the Dyson–Schwinger equations. Such a choice results in good agreement, in the proper limit, with the spectrum of the local theory. We derive a gap equation for the fermions in the theory that gives some indication of quark confinement in the non-local NJL case as well. Confinement seems to be a rather ubiquitous effect that removes some degrees of freedom in the original action, favouring the appearance of new observable states, as seen, e.g., for quantum chromodynamics at lower energies. Full article

The Schwinger confinement mechanism stipulates that a massless fermion and a massless antifermion are confined as a massive boson when they interact in the Abelian QED interaction in (1+1)D.If we approximate light quarks as massless and apply the Schwinger confinement mechanism to quarks, we can infer that a light quark and a light antiquark interacting in the Abelian QED interaction are confined as a QED meson in (1+1)D. Similarly, a light quark and a light antiquark interacting in the QCD interaction in the quasi-Abelian approximation will be confined as a QCD meson in (1+1)D. The QED and QCD mesons in (1+1)D can represent physical mesons in (3+1)D when the flux tube radius is properly taken into account. Such a theory leads to a reasonable description of the masses of ${\pi }^0,\eta$, and ${\eta }^{\prime }$, and its extrapolation to the unknown QED sector yields an isoscalar QED meson at about 17 MeV and an isovector QED meson at about 38 MeV. The observations of the anomalous soft photons, the hypothetical X17 particle, and the hypothetical E38 particle bear promising evidence for the possible existence of the QED mesons. Pending further confirmation, they hold important implications on the properties on the quarks and their interactions. Full article

The Standard Model of electroweak interactions is based on the fundamental SU(2)_weak × U(1)_elect representation. It assumes massless neutrinos and purely left-handed massive $W^{\pm }$ and Z⁰ bosons to which one should add the massless photon. The existence, verified experimentally, of neutrino oscillations poses a challenge to this scheme, since the oscillations take place between at least three massive neutrinos belonging to a mass hierarchy still to be determined. One should also take into account the possible existence of sterile neutrino species. In a somehow different context, the fundamental nature of the strong interaction component of the forces in nature is described by the, until now, extremely successful representation based on the SU(3)_strong group which, together with the confining rule, give a description of massive hadrons in terms of quarks and gluons. To this is added the minimal U(1) Higgs group to give mass to the otherwise massless generators. This representation may also be challenged by the existence of both dark matter and dark energy, of still unknown composition. In this note, we shall discuss a possible connection between these questions, namely the need to extend the SU(3)_strong × SU(2)_weak × U(1)_elect to account for massive neutrinos and dark matter. The main point of it is related to the role of axions, as postulated by Roberto Peccei and Helen Quinn. The existence of neutral pseudo-scalar bosons, that is, the axions, has been proposed long ago by Peccei and Quinn to explain the suppression of the electric dipole moment of the neutron. The associated U(1)_PQ symmetry breaks at very high energy, and it guarantees that the interaction of other particles with axions is very weak. We shall review the axion properties in connection with the apparently different contexts of neutrino and dark matter physics. Full article

An attempt is made to describe from first principles the large-scale structure of the confining vacuum in quantum chromodynamics. Starting from our previous variational studies of the SU(2) pure gauge theory in an external Abelian chromomagnetic field and extending Feynman’s qualitative analysis in (2+1)-dimensional SU(2) gauge theory, we show that the SU(3) vacuum in three-space and one-time dimensions behaves like a disordered chromomagnetic condensate. Color confinement is assured by the presence of a mass gap together with the absence of color long-range correlations. We offer a clear physical picture for the formation of the flux tube between static quark charges that allows us to determine the color structure and the transverse profile of the flux-tube chromoelectric field. The transverse profile of the flux-tube chromoelectric field turns out to be in reasonable agreement with lattice data. We, also, show that our quantum vacuum allows for both the color and ordinary Meissner effect. We find that for massless quarks, the quantum vacuum can accommodate a finite non-zero density of fermion zero modes leading to the dynamical breaking of the chiral symmetry. Full article

Despite the obvious progress made by the Feynman, Ravndal, and Kislinger relativistic model in describing the internal motion of a system with confinement of quarks in a nucleon, it turned out to be insufficiently realistic for a number of reasons. In particular, the model does not take into account some cornerstone properties of QCD, namely, gluon exchange between quarks, the influence of the resulting quark sea on valence quarks, and the self-interaction of colored gluons. It is these phenomena that spontaneously break the chiral symmetry of the quark system and form the bulk of the nucleon. To eliminate the above shortcomings of the model, the problem of self-organization of a three-quark dynamical system immersed in a colored quark–antiquark sea is considered within the framework of complex probabilistic processes that satisfy the stochastic differential equation of the Langevin–Kline–Gordon–Fock type. Taking into account the hidden symmetry of the internal motion of a dynamical system, a mathematically closed nonperturbative approach was developed, which makes it possible to construct the mathematical expectation of the wave function and other parameters of the nucleon in the form of multiple integral representations. It is shown that additional subspaces arising in a representation characterized by a noncommutative geometry with topological features participate in the formation of an effective interaction between valence quarks against the background of harmonic interaction between them. Full article

The aim of this text is to present the covariant confined quark model (CCQM) and review its applications in the decays of B mesons. We do so in the context of existing experimental measurements and theoretical results of other authors, which we also review. The physics principles are, in detail, exposed for the CCQM; the other results (theoretical and experimental) are surveyed in an enumerative way with comments. We proceed by considering, successively, three categories of decay processes: leptonic, semileptonic and non-leptonic. Full article

We study the role of short-range correlations, as well as pion and rho loops governing long-range RPA correlations, in nuclear matter properties and response functions. We use an adapted formulation of the Brueckner G-matrix approach to generate a pair correlation function satisfying the Beg–Agassi–Gal theorem, providing a natural cutoff to the loop integrals. We present results for the case of a relativistic chiral theory, including the effects of quark confinement and of the chirally broken vacuum in a version where parameters are directly connected to QCD observables or constrained by well-established hadron phenomenology. This provides a unified and coherent view of the nuclear matter equation of state and the effect of correlations on neutrino–nucleus scattering. Full article

As known, the realistic, exponential, fall-off of the rate of production of light mesons in the chromo-electric field of a quark–antiquark string, as a function of the meson mass, can be obtained from the Schwinger-formula Gaussian fall-off within a phenomenological approach which assumes a certain distribution of the string tension. This approach gets a clear meaning in the London limit of the dual superconductor, where the logarithmic increase of the chromo-electric field towards the core of the string leads precisely to the change of the Gaussian fall-off to the exponential one, thus allowing for an identification of the phenomenological distribution of the string tension. In this paper, we demonstrate that, for this distribution of the string tension, the distribution of large-size Yang–Mills instantons, which are interacting with the confining monopole background, becomes $\mathcal{O}(1/{\rho }^3)$, where $\rho$ is the size of an instanton. Since such a distribution of large-size instantons is known to yield confinement, we conclude that, in the London limit of the dual-superconductor vacuum, instantons can form a confining medium, and we evaluate their contribution to the total string tension. Full article

The photon production by conversion of gluons $gg\to \gamma$ via quark loop in the framework of the mean-field approach to the QCD (quantunm chromodynamics) vacuum is studied here. According to the domain model of QCD vacuum, the confinement phase is dominated by Abelian (anti-)self-dual gluon fields, while the deconfinement phase is characterized by a strong chromomagnetic field. In the confinement phase, photon production is impossible due to the random spacial orientation of the statistical ensemble of vacuum fields. However, the conditions of Furry theorem are not satisfied in the deconfinement phase, the conversion of gluons is nonzero and, in addition, photon distribution has a strong angular anisotropy. Thus, the photon production in the discussed process acts as one of the important features of transition in quark-gluon plasma to the deconfinement phase. Full article

In 1978, Friedberg and Lee introduced the phenomenological soliton bag model of hadrons, generalizing the MIT bag model developed in 1974 shortly after the formulation of QCD. In this model, quarks and gluons are confined due to coupling with a real scalar field $\rho$, which tends to zero outside some compact region $S\subset {\mathbb{R}}^3$ determined dynamically from the equations of motion. The gauge coupling in the soliton bag model runs as the inverse power of $\rho$, already at the semiclassical level. We show that this model arises naturally as a consequence of introducing the warped product metric $\mathrm{d}{s}_M^2+{\rho }^2\mathrm{d}{s}_G^2$ on the principal G-bundle $P(M,G)\cong M\times G$ with a non-Abelian group G over Minkowski space $M={\mathbb{R}}^{3,1}$. Confinement of quarks and gluons in a compact domain $S\subset {\mathbb{R}}^3$ is a consequence of the collapse of the bundle manifold $M\times G$ to M outside S due to shrinking of the group manifold G to a point. We describe the formation of such regions S as a dynamical process controlled by the order parameter field $\rho$. Full article

In this study, we discuss how iterative solutions of QCD-inspired gap-equations at the finite chemical potential demonstrate domains of chaotic behavior as well as non-chaotic domains, which represent one or the other of the only two—usually distinct—positive mass gap solutions with broken or restored chiral symmetry, respectively. In the iterative approach, gap solutions exist which exhibit restored chiral symmetry beyond a certain dynamical cut-off energy. A chirally broken, non-chaotic domain with no emergent mass poles and hence with no quasi-particle excitations exists below this energy cut-off. The transition domain between these two energy-separated domains is chaotic. As a result, the dispersion relation is that of quarks with restored chiral symmetry, cut at a dynamical energy scale, and determined by fractal structures. We argue that the chaotic origin of the infrared cut-off could hint at a chaotic nature of confinement and the deconfinement phase transition. Full article

The temperature dependence of the QCD string-breaking distance is evaluated in terms of the string tension and the rate of production of light mesons in the chromo-electric field of a flux tube. As a function of the meson mass, the mentioned rate can be falling off either as a Gaussian, as suggested by the Schwinger formula, or as an exponential, which is the case in the London limit of the dual superconductor. We find an excellent agreement of the so-evaluated temperature dependence of the string-breaking distance with the respective lattice data, for the case of the meson-production rate corresponding to the London limit. Full article

Recently, persistent homology analysis has been used to investigate phase structure. In this study, we apply persistent homology analysis to the QCD effective model with heavy quarks at finite imaginary chemical potential; i.e., the Potts model with the suitably tuned external field. Since we try to obtain a deeper understanding of the relationship between persistent homology and phase transition in QCD, we consider the imaginary chemical potential because the clear phase transition, which is closely related to the confinement-deconfinement transition, exists. In the actual analysis, we employ the point-cloud approach to consider persistent homology. In addition, we investigate the fluctuation of persistent diagrams to obtain additional information on the relationship between the spatial topology and the phase transition. Full article

Visible matter is characterised by a single mass scale; namely, the proton mass. The proton’s existence and structure are supposed to be described by quantum chromodynamics (QCD); yet, absent Higgs boson couplings, chromodynamics is scale-invariant. Thus, if the Standard Model is truly a part of the theory of Nature, then the proton mass is an emergent feature of QCD; and emergent hadron mass (EHM) must provide the basic link between theory and observation. Nonperturbative tools are necessary if such connections are to be made; and in this context, we sketch recent progress in the application of continuum Schwinger function methods to an array of related problems in hadron and particle physics. Special emphasis is given to the three pillars of EHM—namely, the running gluon mass, process-independent effective charge, and running quark mass; their role in stabilising QCD; and their measurable expressions in a diverse array of observables. Full article

We generalize a recently proposed confining relativistic density-functional approach to the case of density-dependent vector and diquark couplings. The particular behavior of these couplings is motivated by the non-perturbative gluon exchange in dense quark matter and provides the conformal limit at asymptotically high densities. We demonstrate that this feature of the quark matter EoS is consistent with a significant stiffness in the density range typical for the interiors of neutron stars. In order to model these astrophysical objects, we construct a family of hybrid quark-hadron EoSs of cold stellar matter. We also confront our approach with the observational constraints on the mass–radius relation of neutron stars and their tidal deformabilities and argue in favor of a quark matter onset at masses below $1.0{\mathrm{M}}_{\odot }$. Full article